Relaxion Monodromy and the Weak Gravity Conjecture

TL;DR

This paper explores how relaxion models with monodromy can be consistent with the weak gravity conjecture, analyzing constraints from membrane nucleation and potential string theory embeddings.

Contribution

It introduces a monodromy-based framework for relaxion models, connecting axion shift symmetry, 3-form fields, and the weak gravity conjecture constraints.

Findings

Membrane nucleation constrains relaxion models.

Weak gravity conjecture imposes bounds on model parameters.

Potential string theory embeddings are discussed.

Abstract

The recently proposed relaxion models require extremely large trans-Planckian axion excursions as well as a potential explicitly violating the axion shift symmetry. The latter property is however inconsistent with the axion periodicity, which corresponds to a gauged discrete shift symmetry. A way to make things consistent is to use monodromy, i.e. both the axion and the potential parameters transform under the discrete shift symmetry. The structure is better described in terms of a 3-form field $C_{\mu \nu \rho}$ coupling to the SM Higgs through its field strength $F_4$. The 4-form also couples linearly to the relaxion, in the Kaloper-Sorbo fashion. The extremely small relaxion-Higgs coupling arises in a see-saw fashion as $g\simeq F_4/f$, with $f$ being the axion decay constant. We discuss constraints on this type of constructions from membrane nucleation and the Weak Gravity Conjecture. The latter requires the existence of membranes, whose too fast nucleation could in principle drive the theory out of control, unless the cut-off scale is lowered. This allows to constrain relaxion models on purely theoretical grounds. We also discuss possible avenues to embed this structure into string theory.